Help with Hard newspaper puzzle

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Help with Hard newspaper puzzle

Postby Snowman9000 » Tue Mar 07, 2017 12:21 am

Hi, I'm new to sudoku. I'm reading up on the many strategies. The various "wings" and such. I'm trying to solve the puzzle below, and am stumped. There seems to be one or more long chains, but I don't know what to do with them, without guessing. I'd love some guidance on what particular strategy I need to apply here. Thanks!
edit to add: Shaw Chicago suburban newpapers, March 2, 2017.

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Re: Help with Hard newspaper puzzle

Postby JasonLion » Tue Mar 07, 2017 4:13 am

A remote pair will make progress, and a BUG+1 a few moves later will open a clear path to the solution.

7.1524.894259.8.719..71.45281.4.5297.7.18.534..427.816147852963...341728...697145
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Re: Help with Hard newspaper puzzle

Postby Leren » Tue Mar 07, 2017 6:22 am

It looks like you've missed an easy elimination : a claiming pair of 6's in r13c2 removes the 6 in r3c3.

Next, a 2 stringed Kite (or simple X chain if you like) in 3's solves r3c3 :

Code: Select all
*--------------------------------------------------------------*
| 7     36    1      | 5     2     4      | 36    8     9      |
| 4     2     5      | 9     36    8      | 36    7     1      |
| 9     368   8-3    | 7     1    d36     | 4     5     2      |
|--------------------+--------------------+--------------------|
| 8     1    a36     | 4    b36    5      | 2     9     7      |
| 26    7     269    | 1     8     69     | 5     3     4      |
| 35    59    4      | 2     7    c39     | 8     1     6      |
|--------------------+--------------------+--------------------|
| 1     4     7      | 8     5     2      | 9     6     3      |
| 56    59    69     | 3     4     1      | 7     2     8      |
| 23    38    238    | 6     9     7      | 1     4     5      |
*--------------------------------------------------------------*

If you are not familiar with Kites (or X chains), follow the 3's in cells a-b-c-d or reverse the order to d-c-b-a and you'll conclude that at least one of a or d must be 3, so 3 can be removed from r3c3.

This gets you to here (via a hidden single 8 in r9c2), which is called a BUG+1 situation. The * cell r5c3 must be 6 to avoid a BUG situation, which solves the puzzle.

Code: Select all
*-----------------------------------------------------*
| 7    36   1     | 5    2    4     | 36   8    9     |
| 4    2    5     | 9    36   8     | 36   7    1     |
| 9    36   8     | 7    1    36    | 4    5    2     |
|-----------------+-----------------+-----------------|
| 8    1    36    | 4    36   5     | 2    9    7     |
| 26   7   *6-29  | 1    8    69    | 5    3    4     |
| 35   59   4     | 2    7    39    | 8    1    6     |
|-----------------+-----------------+-----------------|
| 1    4    7     | 8    5    2     | 9    6    3     |
| 56   59   69    | 3    4    1     | 7    2    8     |
| 23   8    23    | 6    9    7     | 1    4    5     |
*-----------------------------------------------------*

If you don't understand the BUG principle read about it here.

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Re: Help with Hard newspaper puzzle

Postby Snowman9000 » Tue Mar 07, 2017 2:43 pm

OK, I'm trying to take it one step at a time from your hints.

So the first hint, the remote pairs. I looked that up, used it to the best of my understanding, and it let me solve R3C3 as 8, and R9C2 as 8. Is that correct and complete, as far as using the 36 remote pairs?
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Re: Help with Hard newspaper puzzle

Postby Snowman9000 » Tue Mar 07, 2017 3:38 pm

OK, I got enthused and without waiting I pressed on with the BUG+1. I read an explanation but was still unclear. I watched a plain spoken youtube video on it and understood it.

So using the BUG+1, I was able to make R5C3 a 6, and that solved everything. Thank you both very much. I'm sure I'll be back for more.
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Re: Help with Hard newspaper puzzle

Postby JasonLion » Tue Mar 07, 2017 5:51 pm

Yes, everything your describe is correct.

To be really through: R3C3 gets set to 8 due to the Remote Pair, while R9C2 gets set to 8 due to a hidden single. Then the BUG+1 and singles to the end (or stte).
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Re: Help with Hard newspaper puzzle

Postby eleven » Tue Mar 07, 2017 8:14 pm

Code: Select all
*--------------------------------------*
 |  7   36   1    | 5 2   4   | 36  8 9 |
 |  4   2    5    | 9 36  8   | 36  7 1 |
 |  9   368  38   | 7 1   36  | 4   5 2 |
 |----------------+-----------+---------|
 |  8   1   Y36   | 4 36  5   | 2   9 7 |
 |  2-6 7    269  | 1 8   69  | 5   3 4 |
 | X35  59   4    | 2 7   39  | 8   1 6 |
 |----------------+-----------+---------|
 |  1   4    7    | 8 5   2   | 9   6 3 |
 | Y56  59   9-6  | 3 4   1   | 7   2 8 |
 |  23  38   238  | 6 9   7   | 1   4 5 |
 *--------------------------------------*

Since it was a newspaper puzzle, it probably was intended to be solved by the xy-wing.
If r6c1 is 3, then r4c3 is 6.
If r6c1 is 5, then r8c1 is 6.
So one of r4c3 and r8c1 must be 6, and you can eliminate 6 from r5c1 and r8c3 (because these "see" both Y cells).
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Re: Help with Hard newspaper puzzle

Postby Leren » Tue Mar 07, 2017 8:53 pm

Code: Select all
*-----------------------------------------------------*
| 7    36   1     | 5    2    4     | 36   8    9     |
| 4    2    5     | 9    36   8     | 36   7    1     |
| 9    368  38    | 7    1    36    | 4    5    2     |
|-----------------+-----------------+-----------------|
| 8    1   Y36    | 4    36   5     | 2    9    7     |
|X26   7    269   | 1    8    69    | 5    3    4     |
| 5-3  59   4     | 2    7    39    | 8    1    6     |
|-----------------+-----------------+-----------------|
| 1    4    7     | 8    5    2     | 9    6    3     |
| 56   59   69    | 3    4    1     | 7    2    8     |
|Y23   38   28-3  | 6    9    7     | 1    4    5     |
*-----------------------------------------------------*

I think eleven is right about the intended solving method, although I saw a slightly different XY wing.

Using his style of argument : If r5c1 is 2, r9c1 is 3. If r5c1 is 6, r4c3 is 3, so 1 of r9c1 and r4c3 must be 3 and you can eliminate 3 from r6c1 and r9c3, which solves the puzzle via subsequent singles.

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Re: Help with Hard newspaper puzzle

Postby Snowman9000 » Wed Mar 08, 2017 2:19 am

Thanks, I will look at those too. I've tried to understand XY-Wing but without working on a puzzle. So that helps my understanding of it.
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Re: Help with Hard newspaper puzzle

Postby Leren » Wed Mar 08, 2017 3:03 am

You can read up on XY Wings at a couple of my favorite teaching sites here and here.

Both have good explanations and nice graphical worked examples. Leren
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